Bum hands refers to hands that smell of fecal matter, usually the result of using an inadequate amount of toilet paper coupled with a failure to wash the affected hands.
"Because he lacked bathroom hygiene, the stench of Mr. Watkin's bum hands permeated the room."

"Not only did Mr. Watkin's burp and fart repeatedly, he also had bum hands."
by Waller B. March 17, 2008
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Simply when your hand smells of bum. Due mainly to having too little toilet paper and being too vigorous on the wipe.
Man1: "Pleased to meet you kind sir".

Man2: (Smells Hand) "Fuck me you have obviously wiped your arse with little paper and much vigour, this has given you 'bum hand'. Can I suggest you wash your hands before serving anymore canapes".
by Dr Quim medicine woman December 9, 2009
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